Senior Project Advisor
Christian Lee
Document Type
Project
Publication Date
Spring 2023
Keywords
Double negation, law of the excluded middle, logic, law of non-contradiction, not not, indeterminacy, vagueness
Abstract
According to the law of the excluded middle (hereafter ‘LEM’) any sentence of the form ‘p or not p’ is logically true. In other words, no matter how the work is like in itself, any sentence of this form must be true. Yet the truth of this theorem remains highly controversial. For it appears to be subject to counterexamples. On the other hand, according to the law of non-contradiction, no sentence of the form ‘p and not p’ is true. The law of non-contradiction is an uncontroversial theorem in logic. Yet a simple proof allows us to derive the former from the latter using the rule of double negation. According to this rule, we can infer from not not p that p. The result is that the rule of double negation has been rejected in logical systems that reject LEM. Even with these rejections, double negation seems obviously true. In this paper I discuss the concepts of logic, LEM, double negation, and the law of non-contradiction. Following this are a few reasons for rejecting LEM and double negation with discussion of costs associated with rejecting both. The point of this paper is not to convince you of one side over the other, but rather to allow you to make that choice according to the presented material.
Department
Philosophy
Recommended Citation
Sahota, Jagmeet, "Not Not Double Negation" (2023). WWU Honors College Senior Projects. 677.
https://cedar.wwu.edu/wwu_honors/677
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf